Properties

Label 350.2.h.d.211.3
Level $350$
Weight $2$
Character 350.211
Analytic conductor $2.795$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [350,2,Mod(71,350)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(350, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([6, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("350.71");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 350.h (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.79476407074\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(5\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 3 x^{19} + 15 x^{18} - 30 x^{17} + 145 x^{16} - 194 x^{15} + 1187 x^{14} - 1490 x^{13} + 10170 x^{12} - 13920 x^{11} + 42087 x^{10} - 591 x^{9} + 65635 x^{8} + 120715 x^{7} + \cdots + 400 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 211.3
Root \(-0.0727237 + 0.223820i\) of defining polynomial
Character \(\chi\) \(=\) 350.211
Dual form 350.2.h.d.141.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.809017 - 0.587785i) q^{2} +(-0.0727237 + 0.223820i) q^{3} +(0.309017 - 0.951057i) q^{4} +(1.97315 + 1.05198i) q^{5} +(0.0727237 + 0.223820i) q^{6} +1.00000 q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.38224 + 1.73080i) q^{9} +O(q^{10})\) \(q+(0.809017 - 0.587785i) q^{2} +(-0.0727237 + 0.223820i) q^{3} +(0.309017 - 0.951057i) q^{4} +(1.97315 + 1.05198i) q^{5} +(0.0727237 + 0.223820i) q^{6} +1.00000 q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.38224 + 1.73080i) q^{9} +(2.21465 - 0.308716i) q^{10} +(-2.81931 + 2.04835i) q^{11} +(0.190393 + 0.138329i) q^{12} +(-0.624050 - 0.453399i) q^{13} +(0.809017 - 0.587785i) q^{14} +(-0.378950 + 0.365128i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.149888 + 0.461307i) q^{17} +2.94462 q^{18} +(-2.01429 - 6.19934i) q^{19} +(1.61023 - 1.55150i) q^{20} +(-0.0727237 + 0.223820i) q^{21} +(-1.07688 + 3.31430i) q^{22} +(6.90600 - 5.01750i) q^{23} +0.235339 q^{24} +(2.78666 + 4.15145i) q^{25} -0.771369 q^{26} +(-1.13181 + 0.822310i) q^{27} +(0.309017 - 0.951057i) q^{28} +(-1.84532 + 5.67931i) q^{29} +(-0.0919607 + 0.518136i) q^{30} +(-1.20329 - 3.70335i) q^{31} -1.00000 q^{32} +(-0.253432 - 0.779983i) q^{33} +(0.392411 + 0.285103i) q^{34} +(1.97315 + 1.05198i) q^{35} +(2.38224 - 1.73080i) q^{36} +(-1.06158 - 0.771285i) q^{37} +(-5.27348 - 3.83140i) q^{38} +(0.146863 - 0.106702i) q^{39} +(0.390759 - 2.20166i) q^{40} +(-5.86485 - 4.26106i) q^{41} +(0.0727237 + 0.223820i) q^{42} -7.85350 q^{43} +(1.07688 + 3.31430i) q^{44} +(2.87975 + 5.92122i) q^{45} +(2.63786 - 8.11849i) q^{46} +(-3.48688 + 10.7315i) q^{47} +(0.190393 - 0.138329i) q^{48} +1.00000 q^{49} +(4.69461 + 1.72064i) q^{50} -0.114150 q^{51} +(-0.624050 + 0.453399i) q^{52} +(2.66397 - 8.19887i) q^{53} +(-0.432314 + 1.33053i) q^{54} +(-7.71776 + 1.07583i) q^{55} +(-0.309017 - 0.951057i) q^{56} +1.53403 q^{57} +(1.84532 + 5.67931i) q^{58} +(-8.49774 - 6.17397i) q^{59} +(0.230155 + 0.473234i) q^{60} +(-10.5731 + 7.68182i) q^{61} +(-3.15026 - 2.28880i) q^{62} +(2.38224 + 1.73080i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-0.754377 - 1.55112i) q^{65} +(-0.663493 - 0.482056i) q^{66} +(2.45478 + 7.55504i) q^{67} +0.485047 q^{68} +(0.620790 + 1.91059i) q^{69} +(2.21465 - 0.308716i) q^{70} +(-0.0996959 + 0.306832i) q^{71} +(0.909936 - 2.80050i) q^{72} +(6.07554 - 4.41414i) q^{73} -1.31219 q^{74} +(-1.13184 + 0.321802i) q^{75} -6.51837 q^{76} +(-2.81931 + 2.04835i) q^{77} +(0.0560967 - 0.172648i) q^{78} +(0.331230 - 1.01942i) q^{79} +(-0.977973 - 2.01086i) q^{80} +(2.62807 + 8.08836i) q^{81} -7.24935 q^{82} +(-1.48918 - 4.58323i) q^{83} +(0.190393 + 0.138329i) q^{84} +(-0.189536 + 1.06791i) q^{85} +(-6.35362 + 4.61617i) q^{86} +(-1.13695 - 0.826040i) q^{87} +(2.81931 + 2.04835i) q^{88} +(-9.89994 + 7.19273i) q^{89} +(5.81017 + 3.09769i) q^{90} +(-0.624050 - 0.453399i) q^{91} +(-2.63786 - 8.11849i) q^{92} +0.916393 q^{93} +(3.48688 + 10.7315i) q^{94} +(2.54711 - 14.3512i) q^{95} +(0.0727237 - 0.223820i) q^{96} +(-0.340108 + 1.04675i) q^{97} +(0.809017 - 0.587785i) q^{98} -10.2616 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 5 q^{2} + 3 q^{3} - 5 q^{4} - 5 q^{5} - 3 q^{6} + 20 q^{7} + 5 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 5 q^{2} + 3 q^{3} - 5 q^{4} - 5 q^{5} - 3 q^{6} + 20 q^{7} + 5 q^{8} - 6 q^{9} - 9 q^{11} - 2 q^{12} + 5 q^{13} + 5 q^{14} - 5 q^{16} - 12 q^{17} - 34 q^{18} + 2 q^{19} + 5 q^{20} + 3 q^{21} - 6 q^{22} - 5 q^{23} + 2 q^{24} - 35 q^{25} + 20 q^{26} - 6 q^{27} - 5 q^{28} - 22 q^{29} - 25 q^{30} - 7 q^{31} - 20 q^{32} + 25 q^{33} - 18 q^{34} - 5 q^{35} - 6 q^{36} - 3 q^{37} + 8 q^{38} - 22 q^{39} + 19 q^{41} - 3 q^{42} + 2 q^{43} + 6 q^{44} + 45 q^{45} - 10 q^{46} - 14 q^{47} - 2 q^{48} + 20 q^{49} + 10 q^{50} + 38 q^{51} + 5 q^{52} - q^{53} - 19 q^{54} - 20 q^{55} + 5 q^{56} + 116 q^{57} + 22 q^{58} + 17 q^{59} - 5 q^{60} - 38 q^{61} + 7 q^{62} - 6 q^{63} - 5 q^{64} + 15 q^{65} - 16 q^{67} - 12 q^{68} + 35 q^{69} + q^{71} + 11 q^{72} + 19 q^{73} + 18 q^{74} + 35 q^{75} + 12 q^{76} - 9 q^{77} - 18 q^{78} - 64 q^{79} - 40 q^{81} + 26 q^{82} + 57 q^{83} - 2 q^{84} - 40 q^{85} - 2 q^{86} - 78 q^{87} + 9 q^{88} - 6 q^{89} + 10 q^{90} + 5 q^{91} + 10 q^{92} - 22 q^{93} + 14 q^{94} + 60 q^{95} - 3 q^{96} - 18 q^{97} + 5 q^{98} + 112 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.809017 0.587785i 0.572061 0.415627i
\(3\) −0.0727237 + 0.223820i −0.0419870 + 0.129223i −0.969853 0.243692i \(-0.921642\pi\)
0.927866 + 0.372914i \(0.121642\pi\)
\(4\) 0.309017 0.951057i 0.154508 0.475528i
\(5\) 1.97315 + 1.05198i 0.882420 + 0.470462i
\(6\) 0.0727237 + 0.223820i 0.0296893 + 0.0913743i
\(7\) 1.00000 0.377964
\(8\) −0.309017 0.951057i −0.109254 0.336249i
\(9\) 2.38224 + 1.73080i 0.794081 + 0.576934i
\(10\) 2.21465 0.308716i 0.700335 0.0976247i
\(11\) −2.81931 + 2.04835i −0.850054 + 0.617601i −0.925161 0.379575i \(-0.876070\pi\)
0.0751066 + 0.997176i \(0.476070\pi\)
\(12\) 0.190393 + 0.138329i 0.0549617 + 0.0399320i
\(13\) −0.624050 0.453399i −0.173080 0.125750i 0.497873 0.867250i \(-0.334115\pi\)
−0.670953 + 0.741500i \(0.734115\pi\)
\(14\) 0.809017 0.587785i 0.216219 0.157092i
\(15\) −0.378950 + 0.365128i −0.0978446 + 0.0942755i
\(16\) −0.809017 0.587785i −0.202254 0.146946i
\(17\) 0.149888 + 0.461307i 0.0363531 + 0.111883i 0.967586 0.252540i \(-0.0812660\pi\)
−0.931233 + 0.364424i \(0.881266\pi\)
\(18\) 2.94462 0.694053
\(19\) −2.01429 6.19934i −0.462109 1.42223i −0.862582 0.505918i \(-0.831154\pi\)
0.400472 0.916309i \(-0.368846\pi\)
\(20\) 1.61023 1.55150i 0.360059 0.346926i
\(21\) −0.0727237 + 0.223820i −0.0158696 + 0.0488416i
\(22\) −1.07688 + 3.31430i −0.229592 + 0.706611i
\(23\) 6.90600 5.01750i 1.44000 1.04622i 0.451958 0.892039i \(-0.350726\pi\)
0.988042 0.154182i \(-0.0492743\pi\)
\(24\) 0.235339 0.0480383
\(25\) 2.78666 + 4.15145i 0.557332 + 0.830290i
\(26\) −0.771369 −0.151278
\(27\) −1.13181 + 0.822310i −0.217818 + 0.158254i
\(28\) 0.309017 0.951057i 0.0583987 0.179733i
\(29\) −1.84532 + 5.67931i −0.342667 + 1.05462i 0.620154 + 0.784480i \(0.287070\pi\)
−0.962821 + 0.270141i \(0.912930\pi\)
\(30\) −0.0919607 + 0.518136i −0.0167897 + 0.0945982i
\(31\) −1.20329 3.70335i −0.216118 0.665142i −0.999072 0.0430629i \(-0.986288\pi\)
0.782955 0.622079i \(-0.213712\pi\)
\(32\) −1.00000 −0.176777
\(33\) −0.253432 0.779983i −0.0441168 0.135778i
\(34\) 0.392411 + 0.285103i 0.0672980 + 0.0488948i
\(35\) 1.97315 + 1.05198i 0.333524 + 0.177818i
\(36\) 2.38224 1.73080i 0.397041 0.288467i
\(37\) −1.06158 0.771285i −0.174523 0.126798i 0.497095 0.867696i \(-0.334400\pi\)
−0.671618 + 0.740898i \(0.734400\pi\)
\(38\) −5.27348 3.83140i −0.855471 0.621536i
\(39\) 0.146863 0.106702i 0.0235169 0.0170860i
\(40\) 0.390759 2.20166i 0.0617844 0.348113i
\(41\) −5.86485 4.26106i −0.915935 0.665466i 0.0265738 0.999647i \(-0.491540\pi\)
−0.942509 + 0.334181i \(0.891540\pi\)
\(42\) 0.0727237 + 0.223820i 0.0112215 + 0.0345362i
\(43\) −7.85350 −1.19765 −0.598824 0.800881i \(-0.704365\pi\)
−0.598824 + 0.800881i \(0.704365\pi\)
\(44\) 1.07688 + 3.31430i 0.162346 + 0.499649i
\(45\) 2.87975 + 5.92122i 0.429288 + 0.882683i
\(46\) 2.63786 8.11849i 0.388931 1.19701i
\(47\) −3.48688 + 10.7315i −0.508613 + 1.56535i 0.285998 + 0.958230i \(0.407675\pi\)
−0.794611 + 0.607120i \(0.792325\pi\)
\(48\) 0.190393 0.138329i 0.0274809 0.0199660i
\(49\) 1.00000 0.142857
\(50\) 4.69461 + 1.72064i 0.663919 + 0.243335i
\(51\) −0.114150 −0.0159842
\(52\) −0.624050 + 0.453399i −0.0865402 + 0.0628751i
\(53\) 2.66397 8.19887i 0.365925 1.12620i −0.583475 0.812131i \(-0.698307\pi\)
0.949400 0.314070i \(-0.101693\pi\)
\(54\) −0.432314 + 1.33053i −0.0588305 + 0.181062i
\(55\) −7.71776 + 1.07583i −1.04066 + 0.145065i
\(56\) −0.309017 0.951057i −0.0412941 0.127090i
\(57\) 1.53403 0.203187
\(58\) 1.84532 + 5.67931i 0.242302 + 0.745729i
\(59\) −8.49774 6.17397i −1.10631 0.803782i −0.124232 0.992253i \(-0.539647\pi\)
−0.982079 + 0.188471i \(0.939647\pi\)
\(60\) 0.230155 + 0.473234i 0.0297129 + 0.0610942i
\(61\) −10.5731 + 7.68182i −1.35375 + 0.983556i −0.354934 + 0.934891i \(0.615497\pi\)
−0.998815 + 0.0486646i \(0.984503\pi\)
\(62\) −3.15026 2.28880i −0.400083 0.290678i
\(63\) 2.38224 + 1.73080i 0.300135 + 0.218061i
\(64\) −0.809017 + 0.587785i −0.101127 + 0.0734732i
\(65\) −0.754377 1.55112i −0.0935690 0.192392i
\(66\) −0.663493 0.482056i −0.0816703 0.0593370i
\(67\) 2.45478 + 7.55504i 0.299899 + 0.922996i 0.981532 + 0.191301i \(0.0612705\pi\)
−0.681632 + 0.731695i \(0.738730\pi\)
\(68\) 0.485047 0.0588206
\(69\) 0.620790 + 1.91059i 0.0747343 + 0.230009i
\(70\) 2.21465 0.308716i 0.264702 0.0368987i
\(71\) −0.0996959 + 0.306832i −0.0118317 + 0.0364143i −0.956798 0.290753i \(-0.906094\pi\)
0.944966 + 0.327168i \(0.106094\pi\)
\(72\) 0.909936 2.80050i 0.107237 0.330042i
\(73\) 6.07554 4.41414i 0.711088 0.516636i −0.172436 0.985021i \(-0.555164\pi\)
0.883525 + 0.468385i \(0.155164\pi\)
\(74\) −1.31219 −0.152539
\(75\) −1.13184 + 0.321802i −0.130693 + 0.0371585i
\(76\) −6.51837 −0.747709
\(77\) −2.81931 + 2.04835i −0.321290 + 0.233431i
\(78\) 0.0560967 0.172648i 0.00635170 0.0195485i
\(79\) 0.331230 1.01942i 0.0372662 0.114694i −0.930693 0.365802i \(-0.880795\pi\)
0.967959 + 0.251108i \(0.0807949\pi\)
\(80\) −0.977973 2.01086i −0.109341 0.224821i
\(81\) 2.62807 + 8.08836i 0.292008 + 0.898707i
\(82\) −7.24935 −0.800557
\(83\) −1.48918 4.58323i −0.163459 0.503074i 0.835461 0.549550i \(-0.185201\pi\)
−0.998919 + 0.0464759i \(0.985201\pi\)
\(84\) 0.190393 + 0.138329i 0.0207736 + 0.0150929i
\(85\) −0.189536 + 1.06791i −0.0205581 + 0.115831i
\(86\) −6.35362 + 4.61617i −0.685128 + 0.497775i
\(87\) −1.13695 0.826040i −0.121893 0.0885608i
\(88\) 2.81931 + 2.04835i 0.300540 + 0.218355i
\(89\) −9.89994 + 7.19273i −1.04939 + 0.762428i −0.972097 0.234581i \(-0.924628\pi\)
−0.0772949 + 0.997008i \(0.524628\pi\)
\(90\) 5.81017 + 3.09769i 0.612446 + 0.326525i
\(91\) −0.624050 0.453399i −0.0654182 0.0475291i
\(92\) −2.63786 8.11849i −0.275016 0.846411i
\(93\) 0.916393 0.0950256
\(94\) 3.48688 + 10.7315i 0.359644 + 1.10687i
\(95\) 2.54711 14.3512i 0.261328 1.47241i
\(96\) 0.0727237 0.223820i 0.00742233 0.0228436i
\(97\) −0.340108 + 1.04675i −0.0345328 + 0.106281i −0.966837 0.255394i \(-0.917795\pi\)
0.932304 + 0.361675i \(0.117795\pi\)
\(98\) 0.809017 0.587785i 0.0817231 0.0593753i
\(99\) −10.2616 −1.03133
\(100\) 4.80939 1.36740i 0.480939 0.136740i
\(101\) 13.1146 1.30495 0.652475 0.757811i \(-0.273731\pi\)
0.652475 + 0.757811i \(0.273731\pi\)
\(102\) −0.0923495 + 0.0670959i −0.00914397 + 0.00664348i
\(103\) 2.51189 7.73082i 0.247504 0.761740i −0.747710 0.664025i \(-0.768847\pi\)
0.995214 0.0977148i \(-0.0311533\pi\)
\(104\) −0.238366 + 0.733615i −0.0233737 + 0.0719369i
\(105\) −0.378950 + 0.365128i −0.0369818 + 0.0356328i
\(106\) −2.66397 8.19887i −0.258748 0.796344i
\(107\) 18.4064 1.77941 0.889707 0.456533i \(-0.150909\pi\)
0.889707 + 0.456533i \(0.150909\pi\)
\(108\) 0.432314 + 1.33053i 0.0415995 + 0.128030i
\(109\) −11.0616 8.03675i −1.05951 0.769781i −0.0855140 0.996337i \(-0.527253\pi\)
−0.973998 + 0.226556i \(0.927253\pi\)
\(110\) −5.61144 + 5.40675i −0.535030 + 0.515514i
\(111\) 0.249831 0.181513i 0.0237130 0.0172285i
\(112\) −0.809017 0.587785i −0.0764449 0.0555405i
\(113\) 7.29979 + 5.30360i 0.686706 + 0.498921i 0.875576 0.483081i \(-0.160482\pi\)
−0.188870 + 0.982002i \(0.560482\pi\)
\(114\) 1.24105 0.901678i 0.116235 0.0844498i
\(115\) 18.9049 2.63529i 1.76289 0.245742i
\(116\) 4.83111 + 3.51000i 0.448557 + 0.325896i
\(117\) −0.701896 2.16021i −0.0648903 0.199712i
\(118\) −10.5038 −0.966951
\(119\) 0.149888 + 0.461307i 0.0137402 + 0.0422880i
\(120\) 0.464359 + 0.247573i 0.0423900 + 0.0226002i
\(121\) 0.353594 1.08825i 0.0321449 0.0989318i
\(122\) −4.03857 + 12.4294i −0.365635 + 1.12531i
\(123\) 1.38023 1.00279i 0.124451 0.0904187i
\(124\) −3.89393 −0.349686
\(125\) 1.13124 + 11.1230i 0.101181 + 0.994868i
\(126\) 2.94462 0.262327
\(127\) −2.57756 + 1.87271i −0.228721 + 0.166176i −0.696244 0.717805i \(-0.745147\pi\)
0.467522 + 0.883981i \(0.345147\pi\)
\(128\) −0.309017 + 0.951057i −0.0273135 + 0.0840623i
\(129\) 0.571135 1.75777i 0.0502857 0.154763i
\(130\) −1.52203 0.811468i −0.133491 0.0711704i
\(131\) −2.34540 7.21840i −0.204919 0.630675i −0.999717 0.0238006i \(-0.992423\pi\)
0.794798 0.606874i \(-0.207577\pi\)
\(132\) −0.820123 −0.0713825
\(133\) −2.01429 6.19934i −0.174661 0.537551i
\(134\) 6.42670 + 4.66927i 0.555183 + 0.403364i
\(135\) −3.09830 + 0.431894i −0.266659 + 0.0371715i
\(136\) 0.392411 0.285103i 0.0336490 0.0244474i
\(137\) 9.43305 + 6.85351i 0.805919 + 0.585535i 0.912645 0.408754i \(-0.134037\pi\)
−0.106725 + 0.994289i \(0.534037\pi\)
\(138\) 1.62525 + 1.18081i 0.138350 + 0.100517i
\(139\) −6.27726 + 4.56070i −0.532431 + 0.386833i −0.821266 0.570545i \(-0.806732\pi\)
0.288836 + 0.957379i \(0.406732\pi\)
\(140\) 1.61023 1.55150i 0.136090 0.131126i
\(141\) −2.14835 1.56087i −0.180924 0.131449i
\(142\) 0.0996959 + 0.306832i 0.00836630 + 0.0257488i
\(143\) 2.68811 0.224791
\(144\) −0.909936 2.80050i −0.0758280 0.233375i
\(145\) −9.61564 + 9.26489i −0.798535 + 0.769407i
\(146\) 2.32065 7.14223i 0.192058 0.591095i
\(147\) −0.0727237 + 0.223820i −0.00599815 + 0.0184604i
\(148\) −1.06158 + 0.771285i −0.0872616 + 0.0633992i
\(149\) 13.1485 1.07717 0.538584 0.842572i \(-0.318959\pi\)
0.538584 + 0.842572i \(0.318959\pi\)
\(150\) −0.726523 + 0.925619i −0.0593204 + 0.0755765i
\(151\) −13.9998 −1.13929 −0.569645 0.821891i \(-0.692919\pi\)
−0.569645 + 0.821891i \(0.692919\pi\)
\(152\) −5.27348 + 3.83140i −0.427735 + 0.310768i
\(153\) −0.441362 + 1.35837i −0.0356820 + 0.109818i
\(154\) −1.07688 + 3.31430i −0.0867776 + 0.267074i
\(155\) 1.52159 8.57312i 0.122217 0.688610i
\(156\) −0.0560967 0.172648i −0.00449133 0.0138229i
\(157\) 3.25293 0.259612 0.129806 0.991539i \(-0.458565\pi\)
0.129806 + 0.991539i \(0.458565\pi\)
\(158\) −0.331230 1.01942i −0.0263512 0.0811007i
\(159\) 1.64134 + 1.19250i 0.130167 + 0.0945716i
\(160\) −1.97315 1.05198i −0.155991 0.0831667i
\(161\) 6.90600 5.01750i 0.544269 0.395435i
\(162\) 6.88037 + 4.99888i 0.540573 + 0.392749i
\(163\) −7.33643 5.33023i −0.574633 0.417496i 0.262152 0.965027i \(-0.415568\pi\)
−0.836785 + 0.547531i \(0.815568\pi\)
\(164\) −5.86485 + 4.26106i −0.457968 + 0.332733i
\(165\) 0.320470 1.80563i 0.0249486 0.140568i
\(166\) −3.89872 2.83259i −0.302600 0.219852i
\(167\) −3.15691 9.71596i −0.244289 0.751844i −0.995753 0.0920694i \(-0.970652\pi\)
0.751464 0.659774i \(-0.229348\pi\)
\(168\) 0.235339 0.0181568
\(169\) −3.83335 11.7978i −0.294873 0.907527i
\(170\) 0.474363 + 0.975363i 0.0363820 + 0.0748069i
\(171\) 5.93131 18.2547i 0.453578 1.39597i
\(172\) −2.42687 + 7.46912i −0.185047 + 0.569515i
\(173\) 11.3415 8.24009i 0.862280 0.626483i −0.0662246 0.997805i \(-0.521095\pi\)
0.928504 + 0.371322i \(0.121095\pi\)
\(174\) −1.40534 −0.106539
\(175\) 2.78666 + 4.15145i 0.210652 + 0.313820i
\(176\) 3.48486 0.262681
\(177\) 1.99985 1.45297i 0.150318 0.109212i
\(178\) −3.78144 + 11.6381i −0.283431 + 0.872311i
\(179\) 1.93279 5.94852i 0.144464 0.444613i −0.852478 0.522763i \(-0.824901\pi\)
0.996942 + 0.0781498i \(0.0249012\pi\)
\(180\) 6.52131 0.909051i 0.486069 0.0677567i
\(181\) 0.917907 + 2.82503i 0.0682275 + 0.209983i 0.979357 0.202137i \(-0.0647886\pi\)
−0.911130 + 0.412120i \(0.864789\pi\)
\(182\) −0.771369 −0.0571776
\(183\) −0.950432 2.92513i −0.0702580 0.216232i
\(184\) −6.90600 5.01750i −0.509117 0.369895i
\(185\) −1.28328 2.63863i −0.0943489 0.193996i
\(186\) 0.741378 0.538643i 0.0543605 0.0394952i
\(187\) −1.36750 0.993546i −0.100001 0.0726553i
\(188\) 9.12876 + 6.63243i 0.665783 + 0.483720i
\(189\) −1.13181 + 0.822310i −0.0823273 + 0.0598143i
\(190\) −6.37479 13.1076i −0.462476 0.950922i
\(191\) 17.3312 + 12.5918i 1.25404 + 0.911113i 0.998449 0.0556724i \(-0.0177302\pi\)
0.255590 + 0.966785i \(0.417730\pi\)
\(192\) −0.0727237 0.223820i −0.00524838 0.0161528i
\(193\) 21.9963 1.58333 0.791665 0.610956i \(-0.209215\pi\)
0.791665 + 0.610956i \(0.209215\pi\)
\(194\) 0.340108 + 1.04675i 0.0244183 + 0.0751519i
\(195\) 0.402033 0.0560422i 0.0287901 0.00401326i
\(196\) 0.309017 0.951057i 0.0220726 0.0679326i
\(197\) −0.741148 + 2.28102i −0.0528046 + 0.162516i −0.973981 0.226629i \(-0.927229\pi\)
0.921177 + 0.389145i \(0.127229\pi\)
\(198\) −8.30179 + 6.03160i −0.589982 + 0.428647i
\(199\) 0.493350 0.0349727 0.0174863 0.999847i \(-0.494434\pi\)
0.0174863 + 0.999847i \(0.494434\pi\)
\(200\) 3.08714 3.93314i 0.218294 0.278115i
\(201\) −1.86949 −0.131864
\(202\) 10.6099 7.70855i 0.746511 0.542372i
\(203\) −1.84532 + 5.67931i −0.129516 + 0.398609i
\(204\) −0.0352744 + 0.108563i −0.00246970 + 0.00760096i
\(205\) −7.08967 14.5774i −0.495164 1.01813i
\(206\) −2.51189 7.73082i −0.175012 0.538632i
\(207\) 25.1361 1.74708
\(208\) 0.238366 + 0.733615i 0.0165277 + 0.0508671i
\(209\) 18.3773 + 13.3519i 1.27119 + 0.923571i
\(210\) −0.0919607 + 0.518136i −0.00634589 + 0.0357548i
\(211\) −5.05405 + 3.67198i −0.347935 + 0.252790i −0.748002 0.663696i \(-0.768987\pi\)
0.400067 + 0.916486i \(0.368987\pi\)
\(212\) −6.97437 5.06718i −0.479002 0.348015i
\(213\) −0.0614251 0.0446280i −0.00420878 0.00305786i
\(214\) 14.8911 10.8190i 1.01793 0.739572i
\(215\) −15.4962 8.26176i −1.05683 0.563447i
\(216\) 1.13181 + 0.822310i 0.0770101 + 0.0559511i
\(217\) −1.20329 3.70335i −0.0816848 0.251400i
\(218\) −13.6729 −0.926048
\(219\) 0.546139 + 1.68084i 0.0369046 + 0.113581i
\(220\) −1.36174 + 7.67248i −0.0918085 + 0.517278i
\(221\) 0.115619 0.355838i 0.00777736 0.0239362i
\(222\) 0.0954271 0.293694i 0.00640465 0.0197115i
\(223\) −12.2348 + 8.88907i −0.819300 + 0.595256i −0.916512 0.400007i \(-0.869008\pi\)
0.0972120 + 0.995264i \(0.469008\pi\)
\(224\) −1.00000 −0.0668153
\(225\) −0.546837 + 14.7129i −0.0364558 + 0.980861i
\(226\) 9.02303 0.600203
\(227\) 7.74229 5.62510i 0.513874 0.373351i −0.300417 0.953808i \(-0.597126\pi\)
0.814291 + 0.580457i \(0.197126\pi\)
\(228\) 0.474040 1.45895i 0.0313941 0.0966210i
\(229\) 2.86979 8.83232i 0.189641 0.583656i −0.810356 0.585938i \(-0.800726\pi\)
0.999997 + 0.00228175i \(0.000726305\pi\)
\(230\) 13.7454 13.2440i 0.906346 0.873285i
\(231\) −0.253432 0.779983i −0.0166746 0.0513191i
\(232\) 5.97158 0.392053
\(233\) −3.34005 10.2796i −0.218814 0.673441i −0.998861 0.0477193i \(-0.984805\pi\)
0.780047 0.625721i \(-0.215195\pi\)
\(234\) −1.83759 1.33509i −0.120127 0.0872773i
\(235\) −18.1695 + 17.5067i −1.18525 + 1.14201i
\(236\) −8.49774 + 6.17397i −0.553155 + 0.401891i
\(237\) 0.204079 + 0.148272i 0.0132563 + 0.00963129i
\(238\) 0.392411 + 0.285103i 0.0254362 + 0.0184805i
\(239\) −12.3443 + 8.96869i −0.798489 + 0.580136i −0.910471 0.413574i \(-0.864280\pi\)
0.111981 + 0.993710i \(0.464280\pi\)
\(240\) 0.521194 0.0726529i 0.0336429 0.00468973i
\(241\) −4.45908 3.23971i −0.287234 0.208688i 0.434832 0.900511i \(-0.356808\pi\)
−0.722067 + 0.691823i \(0.756808\pi\)
\(242\) −0.353594 1.08825i −0.0227299 0.0699554i
\(243\) −6.19846 −0.397631
\(244\) 4.03857 + 12.4294i 0.258543 + 0.795714i
\(245\) 1.97315 + 1.05198i 0.126060 + 0.0672088i
\(246\) 0.527199 1.62255i 0.0336130 0.103450i
\(247\) −1.55376 + 4.78198i −0.0988633 + 0.304270i
\(248\) −3.15026 + 2.28880i −0.200042 + 0.145339i
\(249\) 1.13412 0.0718718
\(250\) 7.45311 + 8.33374i 0.471376 + 0.527072i
\(251\) 29.4811 1.86083 0.930416 0.366506i \(-0.119446\pi\)
0.930416 + 0.366506i \(0.119446\pi\)
\(252\) 2.38224 1.73080i 0.150067 0.109030i
\(253\) −9.19256 + 28.2918i −0.577932 + 1.77869i
\(254\) −0.984540 + 3.03010i −0.0617755 + 0.190126i
\(255\) −0.225236 0.120084i −0.0141048 0.00751997i
\(256\) 0.309017 + 0.951057i 0.0193136 + 0.0594410i
\(257\) 20.7318 1.29321 0.646607 0.762823i \(-0.276187\pi\)
0.646607 + 0.762823i \(0.276187\pi\)
\(258\) −0.571135 1.75777i −0.0355573 0.109434i
\(259\) −1.06158 0.771285i −0.0659635 0.0479253i
\(260\) −1.70831 + 0.238134i −0.105945 + 0.0147685i
\(261\) −14.2258 + 10.3356i −0.880552 + 0.639758i
\(262\) −6.14034 4.46122i −0.379351 0.275615i
\(263\) 13.5433 + 9.83976i 0.835113 + 0.606745i 0.921001 0.389559i \(-0.127373\pi\)
−0.0858880 + 0.996305i \(0.527373\pi\)
\(264\) −0.663493 + 0.482056i −0.0408352 + 0.0296685i
\(265\) 13.8815 13.3751i 0.852734 0.821629i
\(266\) −5.27348 3.83140i −0.323338 0.234918i
\(267\) −0.889919 2.73889i −0.0544622 0.167617i
\(268\) 7.94384 0.485248
\(269\) −0.771620 2.37480i −0.0470465 0.144794i 0.924774 0.380518i \(-0.124254\pi\)
−0.971820 + 0.235723i \(0.924254\pi\)
\(270\) −2.25271 + 2.17054i −0.137096 + 0.132095i
\(271\) 4.04834 12.4595i 0.245919 0.756861i −0.749565 0.661931i \(-0.769737\pi\)
0.995484 0.0949303i \(-0.0302628\pi\)
\(272\) 0.149888 0.461307i 0.00908828 0.0279709i
\(273\) 0.146863 0.106702i 0.00888856 0.00645792i
\(274\) 11.6599 0.704399
\(275\) −16.3601 5.99618i −0.986550 0.361583i
\(276\) 2.00892 0.120923
\(277\) −13.3220 + 9.67902i −0.800443 + 0.581556i −0.911044 0.412309i \(-0.864722\pi\)
0.110601 + 0.993865i \(0.464722\pi\)
\(278\) −2.39770 + 7.37937i −0.143805 + 0.442585i
\(279\) 3.54323 10.9049i 0.212128 0.652862i
\(280\) 0.390759 2.20166i 0.0233523 0.131574i
\(281\) 7.01947 + 21.6037i 0.418747 + 1.28877i 0.908856 + 0.417109i \(0.136957\pi\)
−0.490110 + 0.871661i \(0.663043\pi\)
\(282\) −2.65551 −0.158133
\(283\) 4.45827 + 13.7211i 0.265016 + 0.815637i 0.991690 + 0.128653i \(0.0410655\pi\)
−0.726673 + 0.686983i \(0.758935\pi\)
\(284\) 0.261007 + 0.189633i 0.0154879 + 0.0112526i
\(285\) 3.02687 + 1.61377i 0.179296 + 0.0955915i
\(286\) 2.17473 1.58003i 0.128594 0.0934293i
\(287\) −5.86485 4.26106i −0.346191 0.251522i
\(288\) −2.38224 1.73080i −0.140375 0.101988i
\(289\) 13.5630 9.85406i 0.797821 0.579651i
\(290\) −2.33345 + 13.1474i −0.137025 + 0.772041i
\(291\) −0.209549 0.152246i −0.0122840 0.00892484i
\(292\) −2.32065 7.14223i −0.135806 0.417967i
\(293\) −27.7142 −1.61908 −0.809541 0.587063i \(-0.800284\pi\)
−0.809541 + 0.587063i \(0.800284\pi\)
\(294\) 0.0727237 + 0.223820i 0.00424133 + 0.0130535i
\(295\) −10.2724 21.1217i −0.598083 1.22975i
\(296\) −0.405488 + 1.24797i −0.0235685 + 0.0725365i
\(297\) 1.50655 4.63670i 0.0874192 0.269049i
\(298\) 10.6374 7.72851i 0.616207 0.447700i
\(299\) −6.58462 −0.380798
\(300\) −0.0437042 + 1.17588i −0.00252326 + 0.0678896i
\(301\) −7.85350 −0.452668
\(302\) −11.3261 + 8.22889i −0.651744 + 0.473520i
\(303\) −0.953740 + 2.93531i −0.0547909 + 0.168629i
\(304\) −2.01429 + 6.19934i −0.115527 + 0.355557i
\(305\) −28.9435 + 4.03464i −1.65730 + 0.231023i
\(306\) 0.441362 + 1.35837i 0.0252310 + 0.0776530i
\(307\) −6.11087 −0.348766 −0.174383 0.984678i \(-0.555793\pi\)
−0.174383 + 0.984678i \(0.555793\pi\)
\(308\) 1.07688 + 3.31430i 0.0613610 + 0.188850i
\(309\) 1.54764 + 1.12443i 0.0880422 + 0.0639664i
\(310\) −3.80816 7.83017i −0.216289 0.444724i
\(311\) −17.1278 + 12.4440i −0.971226 + 0.705637i −0.955731 0.294243i \(-0.904933\pi\)
−0.0154954 + 0.999880i \(0.504933\pi\)
\(312\) −0.146863 0.106702i −0.00831449 0.00604083i
\(313\) 5.91106 + 4.29464i 0.334113 + 0.242747i 0.742174 0.670207i \(-0.233795\pi\)
−0.408061 + 0.912955i \(0.633795\pi\)
\(314\) 2.63168 1.91203i 0.148514 0.107902i
\(315\) 2.87975 + 5.92122i 0.162256 + 0.333623i
\(316\) −0.867170 0.630036i −0.0487821 0.0354423i
\(317\) −3.32388 10.2298i −0.186687 0.574565i 0.813286 0.581864i \(-0.197677\pi\)
−0.999973 + 0.00729942i \(0.997677\pi\)
\(318\) 2.02881 0.113770
\(319\) −6.43068 19.7916i −0.360049 1.10812i
\(320\) −2.21465 + 0.308716i −0.123803 + 0.0172578i
\(321\) −1.33858 + 4.11973i −0.0747123 + 0.229941i
\(322\) 2.63786 8.11849i 0.147002 0.452426i
\(323\) 2.55788 1.85841i 0.142324 0.103405i
\(324\) 8.50461 0.472478
\(325\) 0.143249 3.85418i 0.00794602 0.213792i
\(326\) −9.06832 −0.502248
\(327\) 2.60323 1.89136i 0.143959 0.104592i
\(328\) −2.24017 + 6.89454i −0.123693 + 0.380687i
\(329\) −3.48688 + 10.7315i −0.192238 + 0.591647i
\(330\) −0.802057 1.64915i −0.0441518 0.0907829i
\(331\) 6.81870 + 20.9858i 0.374790 + 1.15348i 0.943620 + 0.331029i \(0.107396\pi\)
−0.568831 + 0.822455i \(0.692604\pi\)
\(332\) −4.81909 −0.264482
\(333\) −1.19401 3.67478i −0.0654312 0.201377i
\(334\) −8.26489 6.00480i −0.452235 0.328568i
\(335\) −3.10413 + 17.4896i −0.169597 + 0.955561i
\(336\) 0.190393 0.138329i 0.0103868 0.00754644i
\(337\) −24.7357 17.9716i −1.34744 0.978973i −0.999135 0.0415919i \(-0.986757\pi\)
−0.348306 0.937381i \(-0.613243\pi\)
\(338\) −10.0358 7.29147i −0.545878 0.396604i
\(339\) −1.71792 + 1.24814i −0.0933047 + 0.0677898i
\(340\) 0.957071 + 0.510262i 0.0519045 + 0.0276728i
\(341\) 10.9782 + 7.97614i 0.594504 + 0.431932i
\(342\) −5.93131 18.2547i −0.320728 0.987100i
\(343\) 1.00000 0.0539949
\(344\) 2.42687 + 7.46912i 0.130848 + 0.402708i
\(345\) −0.785003 + 4.42295i −0.0422631 + 0.238124i
\(346\) 4.33207 13.3328i 0.232894 0.716773i
\(347\) −4.63033 + 14.2507i −0.248569 + 0.765017i 0.746460 + 0.665430i \(0.231752\pi\)
−0.995029 + 0.0995862i \(0.968248\pi\)
\(348\) −1.13695 + 0.826040i −0.0609467 + 0.0442804i
\(349\) −1.78680 −0.0956453 −0.0478227 0.998856i \(-0.515228\pi\)
−0.0478227 + 0.998856i \(0.515228\pi\)
\(350\) 4.69461 + 1.72064i 0.250938 + 0.0919719i
\(351\) 1.07914 0.0576004
\(352\) 2.81931 2.04835i 0.150270 0.109177i
\(353\) 7.29026 22.4371i 0.388021 1.19421i −0.546244 0.837626i \(-0.683943\pi\)
0.934265 0.356580i \(-0.116057\pi\)
\(354\) 0.763873 2.35096i 0.0405994 0.124952i
\(355\) −0.519498 + 0.500549i −0.0275721 + 0.0265664i
\(356\) 3.78144 + 11.6381i 0.200416 + 0.616817i
\(357\) −0.114150 −0.00604148
\(358\) −1.93279 5.94852i −0.102151 0.314389i
\(359\) −5.85539 4.25419i −0.309036 0.224528i 0.422447 0.906388i \(-0.361171\pi\)
−0.731483 + 0.681860i \(0.761171\pi\)
\(360\) 4.74152 4.56857i 0.249900 0.240785i
\(361\) −19.0032 + 13.8066i −1.00017 + 0.726663i
\(362\) 2.40311 + 1.74596i 0.126305 + 0.0917657i
\(363\) 0.217858 + 0.158283i 0.0114346 + 0.00830771i
\(364\) −0.624050 + 0.453399i −0.0327091 + 0.0237646i
\(365\) 16.6316 2.31839i 0.870536 0.121350i
\(366\) −2.48826 1.80783i −0.130064 0.0944967i
\(367\) −2.66815 8.21172i −0.139276 0.428648i 0.856954 0.515392i \(-0.172354\pi\)
−0.996231 + 0.0867439i \(0.972354\pi\)
\(368\) −8.53628 −0.444985
\(369\) −6.59645 20.3018i −0.343397 1.05687i
\(370\) −2.58915 1.38040i −0.134603 0.0717637i
\(371\) 2.66397 8.19887i 0.138307 0.425664i
\(372\) 0.283181 0.871542i 0.0146823 0.0451873i
\(373\) −21.6341 + 15.7181i −1.12017 + 0.813854i −0.984235 0.176864i \(-0.943405\pi\)
−0.135938 + 0.990717i \(0.543405\pi\)
\(374\) −1.69032 −0.0874044
\(375\) −2.57181 0.555708i −0.132808 0.0286966i
\(376\) 11.2838 0.581916
\(377\) 3.72656 2.70751i 0.191928 0.139444i
\(378\) −0.432314 + 1.33053i −0.0222358 + 0.0684349i
\(379\) −1.22610 + 3.77354i −0.0629804 + 0.193834i −0.977596 0.210491i \(-0.932494\pi\)
0.914615 + 0.404325i \(0.132494\pi\)
\(380\) −12.8617 6.85723i −0.659793 0.351768i
\(381\) −0.231700 0.713100i −0.0118704 0.0365332i
\(382\) 21.4225 1.09607
\(383\) −0.686735 2.11355i −0.0350905 0.107998i 0.931977 0.362517i \(-0.118083\pi\)
−0.967068 + 0.254520i \(0.918083\pi\)
\(384\) −0.190393 0.138329i −0.00971595 0.00705905i
\(385\) −7.71776 + 1.07583i −0.393334 + 0.0548296i
\(386\) 17.7954 12.9291i 0.905762 0.658074i
\(387\) −18.7090 13.5929i −0.951030 0.690964i
\(388\) 0.890415 + 0.646924i 0.0452040 + 0.0328426i
\(389\) 0.744340 0.540795i 0.0377395 0.0274194i −0.568756 0.822507i \(-0.692575\pi\)
0.606495 + 0.795087i \(0.292575\pi\)
\(390\) 0.292310 0.281648i 0.0148017 0.0142618i
\(391\) 3.34973 + 2.43372i 0.169403 + 0.123079i
\(392\) −0.309017 0.951057i −0.0156077 0.0480356i
\(393\) 1.78619 0.0901014
\(394\) 0.741148 + 2.28102i 0.0373385 + 0.114916i
\(395\) 1.72598 1.66302i 0.0868435 0.0836757i
\(396\) −3.17100 + 9.75934i −0.159349 + 0.490425i
\(397\) −8.42926 + 25.9426i −0.423052 + 1.30202i 0.481794 + 0.876284i \(0.339985\pi\)
−0.904847 + 0.425737i \(0.860015\pi\)
\(398\) 0.399129 0.289984i 0.0200065 0.0145356i
\(399\) 1.53403 0.0767973
\(400\) 0.185708 4.99655i 0.00928538 0.249828i
\(401\) −9.12314 −0.455588 −0.227794 0.973709i \(-0.573151\pi\)
−0.227794 + 0.973709i \(0.573151\pi\)
\(402\) −1.51245 + 1.09886i −0.0754343 + 0.0548062i
\(403\) −0.928181 + 2.85665i −0.0462360 + 0.142300i
\(404\) 4.05263 12.4727i 0.201626 0.620540i
\(405\) −3.32325 + 18.7243i −0.165134 + 0.930416i
\(406\) 1.84532 + 5.67931i 0.0915816 + 0.281859i
\(407\) 4.57279 0.226665
\(408\) 0.0352744 + 0.108563i 0.00174634 + 0.00537469i
\(409\) 27.9461 + 20.3040i 1.38185 + 1.00397i 0.996705 + 0.0811129i \(0.0258474\pi\)
0.385142 + 0.922857i \(0.374153\pi\)
\(410\) −14.3041 7.62620i −0.706428 0.376631i
\(411\) −2.21996 + 1.61290i −0.109503 + 0.0795583i
\(412\) −6.57623 4.77791i −0.323987 0.235391i
\(413\) −8.49774 6.17397i −0.418146 0.303801i
\(414\) 20.3355 14.7746i 0.999436 0.726133i
\(415\) 1.88310 10.6100i 0.0924379 0.520824i
\(416\) 0.624050 + 0.453399i 0.0305966 + 0.0222297i
\(417\) −0.564272 1.73665i −0.0276325 0.0850441i
\(418\) 22.7156 1.11106
\(419\) 7.60701 + 23.4120i 0.371627 + 1.14375i 0.945726 + 0.324964i \(0.105352\pi\)
−0.574099 + 0.818786i \(0.694648\pi\)
\(420\) 0.230155 + 0.473234i 0.0112304 + 0.0230914i
\(421\) 0.558083 1.71760i 0.0271993 0.0837108i −0.936535 0.350573i \(-0.885987\pi\)
0.963735 + 0.266862i \(0.0859869\pi\)
\(422\) −1.93047 + 5.94139i −0.0939740 + 0.289222i
\(423\) −26.8807 + 19.5300i −1.30698 + 0.949579i
\(424\) −8.62080 −0.418663
\(425\) −1.49741 + 1.90776i −0.0726349 + 0.0925398i
\(426\) −0.0759256 −0.00367861
\(427\) −10.5731 + 7.68182i −0.511669 + 0.371749i
\(428\) 5.68789 17.5055i 0.274934 0.846161i
\(429\) −0.195489 + 0.601654i −0.00943831 + 0.0290481i
\(430\) −17.3928 + 2.42451i −0.838755 + 0.116920i
\(431\) 9.19050 + 28.2854i 0.442691 + 1.36246i 0.884996 + 0.465598i \(0.154161\pi\)
−0.442306 + 0.896864i \(0.645839\pi\)
\(432\) 1.39900 0.0673093
\(433\) 0.0997250 + 0.306922i 0.00479248 + 0.0147497i 0.953424 0.301633i \(-0.0975317\pi\)
−0.948632 + 0.316383i \(0.897532\pi\)
\(434\) −3.15026 2.28880i −0.151217 0.109866i
\(435\) −1.37439 2.82595i −0.0658968 0.135494i
\(436\) −11.0616 + 8.03675i −0.529756 + 0.384890i
\(437\) −45.0159 32.7060i −2.15340 1.56454i
\(438\) 1.42981 + 1.03882i 0.0683189 + 0.0496366i
\(439\) 21.5492 15.6564i 1.02849 0.747241i 0.0604835 0.998169i \(-0.480736\pi\)
0.968006 + 0.250928i \(0.0807357\pi\)
\(440\) 3.40810 + 7.00758i 0.162475 + 0.334073i
\(441\) 2.38224 + 1.73080i 0.113440 + 0.0824191i
\(442\) −0.115619 0.355838i −0.00549942 0.0169255i
\(443\) −12.0387 −0.571976 −0.285988 0.958233i \(-0.592322\pi\)
−0.285988 + 0.958233i \(0.592322\pi\)
\(444\) −0.0954271 0.293694i −0.00452877 0.0139381i
\(445\) −27.1007 + 3.77776i −1.28470 + 0.179083i
\(446\) −4.67326 + 14.3828i −0.221285 + 0.681046i
\(447\) −0.956209 + 2.94291i −0.0452271 + 0.139195i
\(448\) −0.809017 + 0.587785i −0.0382225 + 0.0277702i
\(449\) 33.9828 1.60375 0.801873 0.597494i \(-0.203837\pi\)
0.801873 + 0.597494i \(0.203837\pi\)
\(450\) 8.20564 + 12.2244i 0.386817 + 0.576265i
\(451\) 25.2630 1.18959
\(452\) 7.29979 5.30360i 0.343353 0.249461i
\(453\) 1.01812 3.13345i 0.0478354 0.147222i
\(454\) 2.95729 9.10160i 0.138793 0.427159i
\(455\) −0.754377 1.55112i −0.0353658 0.0727175i
\(456\) −0.474040 1.45895i −0.0221990 0.0683214i
\(457\) 25.2138 1.17945 0.589726 0.807604i \(-0.299236\pi\)
0.589726 + 0.807604i \(0.299236\pi\)
\(458\) −2.86979 8.83232i −0.134097 0.412707i
\(459\) −0.548983 0.398859i −0.0256243 0.0186172i
\(460\) 3.33563 18.7940i 0.155525 0.876275i
\(461\) 3.36558 2.44524i 0.156751 0.113886i −0.506645 0.862155i \(-0.669115\pi\)
0.663396 + 0.748269i \(0.269115\pi\)
\(462\) −0.663493 0.482056i −0.0308685 0.0224273i
\(463\) −8.78033 6.37929i −0.408057 0.296471i 0.364758 0.931102i \(-0.381152\pi\)
−0.772815 + 0.634632i \(0.781152\pi\)
\(464\) 4.83111 3.51000i 0.224279 0.162948i
\(465\) 1.80818 + 0.964031i 0.0838525 + 0.0447059i
\(466\) −8.74437 6.35316i −0.405075 0.294304i
\(467\) 4.44159 + 13.6698i 0.205532 + 0.632563i 0.999691 + 0.0248529i \(0.00791175\pi\)
−0.794159 + 0.607710i \(0.792088\pi\)
\(468\) −2.27138 −0.104995
\(469\) 2.45478 + 7.55504i 0.113351 + 0.348860i
\(470\) −4.40923 + 24.8430i −0.203383 + 1.14592i
\(471\) −0.236565 + 0.728073i −0.0109003 + 0.0335478i
\(472\) −3.24585 + 9.98969i −0.149402 + 0.459813i
\(473\) 22.1415 16.0867i 1.01807 0.739668i
\(474\) 0.252255 0.0115865
\(475\) 20.1231 25.6377i 0.923312 1.17634i
\(476\) 0.485047 0.0222321
\(477\) 20.5368 14.9209i 0.940317 0.683181i
\(478\) −4.71512 + 14.5116i −0.215665 + 0.663747i
\(479\) −8.00683 + 24.6425i −0.365841 + 1.12594i 0.583611 + 0.812033i \(0.301639\pi\)
−0.949453 + 0.313911i \(0.898361\pi\)
\(480\) 0.378950 0.365128i 0.0172966 0.0166657i
\(481\) 0.312781 + 0.962641i 0.0142616 + 0.0438927i
\(482\) −5.51172 −0.251052
\(483\) 0.620790 + 1.91059i 0.0282469 + 0.0869351i
\(484\) −0.925721 0.672576i −0.0420782 0.0305716i
\(485\) −1.77224 + 1.70760i −0.0804735 + 0.0775381i
\(486\) −5.01466 + 3.64336i −0.227469 + 0.165266i
\(487\) 14.9597 + 10.8688i 0.677887 + 0.492514i 0.872656 0.488335i \(-0.162396\pi\)
−0.194769 + 0.980849i \(0.562396\pi\)
\(488\) 10.5731 + 7.68182i 0.478622 + 0.347740i
\(489\) 1.72655 1.25441i 0.0780771 0.0567263i
\(490\) 2.21465 0.308716i 0.100048 0.0139464i
\(491\) 5.81886 + 4.22765i 0.262601 + 0.190791i 0.711293 0.702895i \(-0.248110\pi\)
−0.448692 + 0.893687i \(0.648110\pi\)
\(492\) −0.527199 1.62255i −0.0237680 0.0731503i
\(493\) −2.89650 −0.130452
\(494\) 1.55376 + 4.78198i 0.0699069 + 0.215151i
\(495\) −20.2476 10.7950i −0.910064 0.485200i
\(496\) −1.20329 + 3.70335i −0.0540294 + 0.166285i
\(497\) −0.0996959 + 0.306832i −0.00447197 + 0.0137633i
\(498\) 0.917521 0.666618i 0.0411151 0.0298719i
\(499\) 20.1574 0.902369 0.451185 0.892431i \(-0.351002\pi\)
0.451185 + 0.892431i \(0.351002\pi\)
\(500\) 10.9281 + 2.36131i 0.488721 + 0.105601i
\(501\) 2.40421 0.107412
\(502\) 23.8507 17.3286i 1.06451 0.773412i
\(503\) −5.77298 + 17.7674i −0.257404 + 0.792209i 0.735942 + 0.677045i \(0.236740\pi\)
−0.993346 + 0.115165i \(0.963260\pi\)
\(504\) 0.909936 2.80050i 0.0405318 0.124744i
\(505\) 25.8771 + 13.7963i 1.15151 + 0.613929i
\(506\) 9.19256 + 28.2918i 0.408659 + 1.25772i
\(507\) 2.91937 0.129654
\(508\) 0.984540 + 3.03010i 0.0436819 + 0.134439i
\(509\) 32.8443 + 23.8628i 1.45580 + 1.05770i 0.984432 + 0.175764i \(0.0562394\pi\)
0.471367 + 0.881937i \(0.343761\pi\)
\(510\) −0.252804 + 0.0352401i −0.0111943 + 0.00156046i
\(511\) 6.07554 4.41414i 0.268766 0.195270i
\(512\) 0.809017 + 0.587785i 0.0357538 + 0.0259767i
\(513\) 7.37758 + 5.36013i 0.325728 + 0.236655i
\(514\) 16.7724 12.1858i 0.739798 0.537495i
\(515\) 13.0890 12.6116i 0.576772 0.555734i
\(516\) −1.49525 1.08636i −0.0658248 0.0478245i
\(517\) −12.1513 37.3978i −0.534412 1.64475i
\(518\) −1.31219 −0.0576542
\(519\) 1.01950 + 3.13771i 0.0447513 + 0.137730i
\(520\) −1.24208 + 1.19678i −0.0544690 + 0.0524821i
\(521\) 6.88288 21.1833i 0.301545 0.928059i −0.679399 0.733769i \(-0.737760\pi\)
0.980944 0.194290i \(-0.0622404\pi\)
\(522\) −5.43375 + 16.7234i −0.237829 + 0.731962i
\(523\) 18.1082 13.1564i 0.791816 0.575288i −0.116686 0.993169i \(-0.537227\pi\)
0.908502 + 0.417881i \(0.137227\pi\)
\(524\) −7.58987 −0.331565
\(525\) −1.13184 + 0.321802i −0.0493973 + 0.0140446i
\(526\) 16.7404 0.729916
\(527\) 1.52802 1.11017i 0.0665618 0.0483599i
\(528\) −0.253432 + 0.779983i −0.0110292 + 0.0339444i
\(529\) 15.4101 47.4274i 0.670005 2.06206i
\(530\) 3.36865 18.9801i 0.146325 0.824441i
\(531\) −9.55777 29.4158i −0.414772 1.27654i
\(532\) −6.51837 −0.282607
\(533\) 1.72800 + 5.31823i 0.0748479 + 0.230358i
\(534\) −2.32984 1.69273i −0.100822 0.0732515i
\(535\) 36.3186 + 19.3632i 1.57019 + 0.837146i
\(536\) 6.42670 4.66927i 0.277591 0.201682i
\(537\) 1.19084 + 0.865196i 0.0513886 + 0.0373360i
\(538\) −2.02013 1.46771i −0.0870939 0.0632774i
\(539\) −2.81931 + 2.04835i −0.121436 + 0.0882287i
\(540\) −0.546671 + 3.08012i −0.0235250 + 0.132547i
\(541\) −26.3123 19.1170i −1.13125 0.821904i −0.145377 0.989376i \(-0.546439\pi\)
−0.985877 + 0.167473i \(0.946439\pi\)
\(542\) −4.04834 12.4595i −0.173891 0.535182i
\(543\) −0.699052 −0.0299992
\(544\) −0.149888 0.461307i −0.00642638 0.0197784i
\(545\) −13.3717 27.4944i −0.572783 1.17773i
\(546\) 0.0560967 0.172648i 0.00240072 0.00738865i
\(547\) 12.6968 39.0768i 0.542876 1.67080i −0.183110 0.983092i \(-0.558616\pi\)
0.725986 0.687709i \(-0.241384\pi\)
\(548\) 9.43305 6.85351i 0.402960 0.292767i
\(549\) −38.4834 −1.64243
\(550\) −16.7600 + 4.76520i −0.714651 + 0.203189i
\(551\) 38.9250 1.65826
\(552\) 1.62525 1.18081i 0.0691752 0.0502587i
\(553\) 0.331230 1.01942i 0.0140853 0.0433501i
\(554\) −5.08856 + 15.6610i −0.216192 + 0.665371i
\(555\) 0.683904 0.0953343i 0.0290301 0.00404672i
\(556\) 2.39770 + 7.37937i 0.101685 + 0.312955i
\(557\) −35.3007 −1.49574 −0.747870 0.663845i \(-0.768923\pi\)
−0.747870 + 0.663845i \(0.768923\pi\)
\(558\) −3.54323 10.9049i −0.149997 0.461643i
\(559\) 4.90098 + 3.56077i 0.207289 + 0.150605i
\(560\) −0.977973 2.01086i −0.0413269 0.0849745i
\(561\) 0.321825 0.233820i 0.0135875 0.00987188i
\(562\) 18.3772 + 13.3518i 0.775196 + 0.563213i
\(563\) 0.0515701 + 0.0374679i 0.00217342 + 0.00157908i 0.588871 0.808227i \(-0.299572\pi\)
−0.586698 + 0.809806i \(0.699572\pi\)
\(564\) −2.14835 + 1.56087i −0.0904618 + 0.0657244i
\(565\) 8.82428 + 18.1441i 0.371240 + 0.763327i
\(566\) 11.6719 + 8.48013i 0.490606 + 0.356446i
\(567\) 2.62807 + 8.08836i 0.110369 + 0.339679i
\(568\) 0.322623 0.0135370
\(569\) −9.88280 30.4161i −0.414309 1.27511i −0.912868 0.408255i \(-0.866137\pi\)
0.498559 0.866856i \(-0.333863\pi\)
\(570\) 3.39734 0.473579i 0.142299 0.0198360i
\(571\) −13.1665 + 40.5224i −0.551002 + 1.69581i 0.155272 + 0.987872i \(0.450375\pi\)
−0.706274 + 0.707939i \(0.749625\pi\)
\(572\) 0.830672 2.55655i 0.0347322 0.106895i
\(573\) −4.07869 + 2.96334i −0.170390 + 0.123796i
\(574\) −7.24935 −0.302582
\(575\) 40.0746 + 14.6878i 1.67122 + 0.612526i
\(576\) −2.94462 −0.122692
\(577\) 1.86947 1.35825i 0.0778270 0.0565446i −0.548191 0.836353i \(-0.684683\pi\)
0.626018 + 0.779808i \(0.284683\pi\)
\(578\) 5.18059 15.9442i 0.215484 0.663192i
\(579\) −1.59965 + 4.92322i −0.0664793 + 0.204602i
\(580\) 5.84004 + 12.0080i 0.242494 + 0.498606i
\(581\) −1.48918 4.58323i −0.0617816 0.190144i
\(582\) −0.259017 −0.0107366
\(583\) 9.28357 + 28.5719i 0.384486 + 1.18333i
\(584\) −6.07554 4.41414i −0.251408 0.182658i
\(585\) 0.887564 5.00082i 0.0366962 0.206758i
\(586\) −22.4213 + 16.2900i −0.926215 + 0.672934i
\(587\) 10.1285 + 7.35882i 0.418050 + 0.303731i 0.776853 0.629682i \(-0.216815\pi\)
−0.358803 + 0.933413i \(0.616815\pi\)
\(588\) 0.190393 + 0.138329i 0.00785167 + 0.00570458i
\(589\) −20.5346 + 14.9192i −0.846112 + 0.614736i
\(590\) −20.7256 11.0498i −0.853257 0.454913i
\(591\) −0.456639 0.331768i −0.0187836 0.0136471i
\(592\) 0.405488 + 1.24797i 0.0166655 + 0.0512911i
\(593\) 34.7754 1.42805 0.714027 0.700118i \(-0.246870\pi\)
0.714027 + 0.700118i \(0.246870\pi\)
\(594\) −1.50655 4.63670i −0.0618147 0.190246i
\(595\) −0.189536 + 1.06791i −0.00777024 + 0.0437800i
\(596\) 4.06312 12.5050i 0.166432 0.512224i
\(597\) −0.0358782 + 0.110422i −0.00146840 + 0.00451927i
\(598\) −5.32707 + 3.87034i −0.217840 + 0.158270i
\(599\) −14.4475 −0.590308 −0.295154 0.955450i \(-0.595371\pi\)
−0.295154 + 0.955450i \(0.595371\pi\)
\(600\) 0.655808 + 0.976997i 0.0267733 + 0.0398857i
\(601\) −13.7849 −0.562298 −0.281149 0.959664i \(-0.590716\pi\)
−0.281149 + 0.959664i \(0.590716\pi\)
\(602\) −6.35362 + 4.61617i −0.258954 + 0.188141i
\(603\) −7.22839 + 22.2467i −0.294363 + 0.905956i
\(604\) −4.32619 + 13.3146i −0.176030 + 0.541765i
\(605\) 1.84252 1.77531i 0.0749090 0.0721765i
\(606\) 0.953740 + 2.93531i 0.0387430 + 0.119239i
\(607\) 24.7641 1.00514 0.502572 0.864535i \(-0.332387\pi\)
0.502572 + 0.864535i \(0.332387\pi\)
\(608\) 2.01429 + 6.19934i 0.0816902 + 0.251417i
\(609\) −1.13695 0.826040i −0.0460714 0.0334728i
\(610\) −21.0443 + 20.2767i −0.852059 + 0.820978i
\(611\) 7.04164 5.11605i 0.284874 0.206973i
\(612\) 1.15550 + 0.839520i 0.0467083 + 0.0339356i
\(613\) −13.0410 9.47485i −0.526721 0.382686i 0.292409 0.956293i \(-0.405543\pi\)
−0.819130 + 0.573608i \(0.805543\pi\)
\(614\) −4.94379 + 3.59188i −0.199515 + 0.144956i
\(615\) 3.77832 0.526686i 0.152356 0.0212380i
\(616\) 2.81931 + 2.04835i 0.113593 + 0.0825304i
\(617\) −13.5170 41.6010i −0.544173 1.67479i −0.722948 0.690903i \(-0.757213\pi\)
0.178775 0.983890i \(-0.442787\pi\)
\(618\) 1.91299 0.0769517
\(619\) −0.756922 2.32957i −0.0304233 0.0936332i 0.934692 0.355459i \(-0.115675\pi\)
−0.965115 + 0.261826i \(0.915675\pi\)
\(620\) −7.68332 4.09636i −0.308570 0.164514i
\(621\) −3.69036 + 11.3578i −0.148089 + 0.455771i
\(622\) −6.54222 + 20.1349i −0.262319 + 0.807335i
\(623\) −9.89994 + 7.19273i −0.396633 + 0.288171i
\(624\) −0.181533 −0.00726713
\(625\) −9.46908 + 23.1373i −0.378763 + 0.925494i
\(626\) 7.30648 0.292026
\(627\) −4.32490 + 3.14222i −0.172720 + 0.125488i
\(628\) 1.00521 3.09372i 0.0401123 0.123453i
\(629\) 0.196681 0.605322i 0.00784218 0.0241358i
\(630\) 5.81017 + 3.09769i 0.231483 + 0.123415i
\(631\) −4.99072 15.3598i −0.198677 0.611466i −0.999914 0.0131183i \(-0.995824\pi\)
0.801237 0.598348i \(-0.204176\pi\)
\(632\) −1.07188 −0.0426372
\(633\) −0.454315 1.39824i −0.0180574 0.0555750i
\(634\) −8.70202 6.32239i −0.345601 0.251094i
\(635\) −7.05598 + 0.983583i −0.280008 + 0.0390323i
\(636\) 1.64134 1.19250i 0.0650833 0.0472858i
\(637\) −0.624050 0.453399i −0.0247258 0.0179643i
\(638\) −16.8357 12.2319i −0.666533 0.484265i
\(639\) −0.768566 + 0.558396i −0.0304040 + 0.0220898i
\(640\) −1.61023 + 1.55150i −0.0636501 + 0.0613283i
\(641\) −23.7578 17.2610i −0.938375 0.681769i 0.00965388 0.999953i \(-0.496927\pi\)
−0.948029 + 0.318184i \(0.896927\pi\)
\(642\) 1.33858 + 4.11973i 0.0528295 + 0.162593i
\(643\) −1.12149 −0.0442273 −0.0221136 0.999755i \(-0.507040\pi\)
−0.0221136 + 0.999755i \(0.507040\pi\)
\(644\) −2.63786 8.11849i −0.103946 0.319913i
\(645\) 2.97609 2.86753i 0.117183 0.112909i
\(646\) 0.977025 3.00697i 0.0384405 0.118308i
\(647\) −10.3490 + 31.8510i −0.406862 + 1.25219i 0.512468 + 0.858706i \(0.328731\pi\)
−0.919330 + 0.393487i \(0.871269\pi\)
\(648\) 6.88037 4.99888i 0.270287 0.196375i
\(649\) 36.6042 1.43684
\(650\) −2.14954 3.20230i −0.0843119 0.125604i
\(651\) 0.916393 0.0359163
\(652\) −7.33643 + 5.33023i −0.287317 + 0.208748i
\(653\) 11.5699 35.6086i 0.452767 1.39347i −0.420970 0.907074i \(-0.638310\pi\)
0.873737 0.486398i \(-0.161690\pi\)
\(654\) 0.994345 3.06028i 0.0388820 0.119666i
\(655\) 2.96581 16.7103i 0.115884 0.652926i
\(656\) 2.24017 + 6.89454i 0.0874640 + 0.269187i
\(657\) 22.1134 0.862727
\(658\) 3.48688 + 10.7315i 0.135933 + 0.418357i
\(659\) −0.596695 0.433524i −0.0232439 0.0168877i 0.576103 0.817377i \(-0.304573\pi\)
−0.599347 + 0.800490i \(0.704573\pi\)
\(660\) −1.61823 0.862756i −0.0629894 0.0335827i
\(661\) −4.33304 + 3.14814i −0.168536 + 0.122448i −0.668856 0.743392i \(-0.733216\pi\)
0.500320 + 0.865840i \(0.333216\pi\)
\(662\) 17.8516 + 12.9699i 0.693822 + 0.504091i
\(663\) 0.0712355 + 0.0517556i 0.00276656 + 0.00201002i
\(664\) −3.89872 + 2.83259i −0.151300 + 0.109926i
\(665\) 2.54711 14.3512i 0.0987728 0.556517i
\(666\) −3.12595 2.27114i −0.121128 0.0880048i
\(667\) 15.7522 + 48.4802i 0.609926 + 1.87716i
\(668\) −10.2160 −0.395268
\(669\) −1.09980 3.38483i −0.0425207 0.130865i
\(670\) 7.76886 + 15.9740i 0.300137 + 0.617129i
\(671\) 14.0739 43.3149i 0.543315 1.67215i
\(672\) 0.0727237 0.223820i 0.00280538 0.00863406i
\(673\) 9.38039 6.81525i 0.361587 0.262709i −0.392127 0.919911i \(-0.628260\pi\)
0.753714 + 0.657203i \(0.228260\pi\)
\(674\) −30.5750 −1.17771
\(675\) −6.56776 2.40717i −0.252793 0.0926519i
\(676\) −12.4050 −0.477115
\(677\) −21.9441 + 15.9433i −0.843381 + 0.612752i −0.923313 0.384048i \(-0.874530\pi\)
0.0799322 + 0.996800i \(0.474530\pi\)
\(678\) −0.656188 + 2.01954i −0.0252007 + 0.0775599i
\(679\) −0.340108 + 1.04675i −0.0130522 + 0.0401704i
\(680\) 1.07421 0.149742i 0.0411941 0.00574234i
\(681\) 0.695965 + 2.14196i 0.0266694 + 0.0820801i
\(682\) 13.5698 0.519615
\(683\) −0.949135 2.92114i −0.0363176 0.111774i 0.931254 0.364370i \(-0.118716\pi\)
−0.967572 + 0.252596i \(0.918716\pi\)
\(684\) −15.5284 11.2820i −0.593742 0.431379i
\(685\) 11.4030 + 23.4464i 0.435688 + 0.895842i
\(686\) 0.809017 0.587785i 0.0308884 0.0224417i
\(687\) 1.76815 + 1.28464i 0.0674592 + 0.0490120i
\(688\) 6.35362 + 4.61617i 0.242229 + 0.175990i
\(689\) −5.37981 + 3.90866i −0.204954 + 0.148908i
\(690\) 1.96467 + 4.03966i 0.0747936 + 0.153787i
\(691\) −28.4788 20.6910i −1.08338 0.787124i −0.105113 0.994460i \(-0.533520\pi\)
−0.978270 + 0.207337i \(0.933520\pi\)
\(692\) −4.33207 13.3328i −0.164681 0.506835i
\(693\) −10.2616 −0.389805
\(694\) 4.63033 + 14.2507i 0.175765 + 0.540948i
\(695\) −17.1838 + 2.39537i −0.651818 + 0.0908616i
\(696\) −0.434275 + 1.33656i −0.0164611 + 0.0506622i
\(697\) 1.08659 3.34418i 0.0411575 0.126670i
\(698\) −1.44555 + 1.05026i −0.0547150 + 0.0397528i
\(699\) 2.54369 0.0962112
\(700\) 4.80939 1.36740i 0.181778 0.0516829i
\(701\) −22.4188 −0.846746 −0.423373 0.905956i \(-0.639154\pi\)
−0.423373 + 0.905956i \(0.639154\pi\)
\(702\) 0.873045 0.634304i 0.0329510 0.0239403i
\(703\) −2.64313 + 8.13470i −0.0996874 + 0.306806i
\(704\) 1.07688 3.31430i 0.0405865 0.124912i
\(705\) −2.59701 5.33986i −0.0978092 0.201111i
\(706\) −7.29026 22.4371i −0.274372 0.844431i
\(707\) 13.1146 0.493224
\(708\) −0.763873 2.35096i −0.0287081 0.0883545i
\(709\) 6.26029 + 4.54837i 0.235110 + 0.170818i 0.699102 0.715022i \(-0.253583\pi\)
−0.463992 + 0.885839i \(0.653583\pi\)
\(710\) −0.126068 + 0.710306i −0.00473124 + 0.0266573i
\(711\) 2.55348 1.85521i 0.0957631 0.0695760i
\(712\) 9.89994 + 7.19273i 0.371016 + 0.269559i
\(713\) −26.8915 19.5378i −1.00709 0.731697i
\(714\) −0.0923495 + 0.0670959i −0.00345610 + 0.00251100i
\(715\) 5.30405 + 2.82785i 0.198360 + 0.105756i
\(716\) −5.06011 3.67639i −0.189105 0.137393i
\(717\) −1.10965 3.41515i −0.0414406 0.127541i
\(718\) −7.23767 −0.270107
\(719\) −13.4264 41.3221i −0.500719 1.54105i −0.807851 0.589387i \(-0.799369\pi\)
0.307132 0.951667i \(-0.400631\pi\)
\(720\) 1.15064 6.48304i 0.0428816 0.241609i
\(721\) 2.51189 7.73082i 0.0935479 0.287911i
\(722\) −7.25856 + 22.3396i −0.270136 + 0.831392i
\(723\) 1.04939 0.762429i 0.0390274 0.0283550i
\(724\) 2.97041 0.110394
\(725\) −28.7196 + 8.16554i −1.06662 + 0.303260i
\(726\) 0.269287 0.00999419
\(727\) −32.0382 + 23.2771i −1.18823 + 0.863302i −0.993076 0.117471i \(-0.962521\pi\)
−0.195156 + 0.980772i \(0.562521\pi\)
\(728\) −0.238366 + 0.733615i −0.00883443 + 0.0271896i
\(729\) −7.43343 + 22.8777i −0.275312 + 0.847324i
\(730\) 12.0925 11.6514i 0.447564 0.431238i
\(731\) −1.17714 3.62288i −0.0435382 0.133997i
\(732\) −3.07566 −0.113680
\(733\) −4.05824 12.4900i −0.149895 0.461328i 0.847713 0.530455i \(-0.177979\pi\)
−0.997608 + 0.0691266i \(0.977979\pi\)
\(734\) −6.98531 5.07512i −0.257832 0.187326i
\(735\) −0.378950 + 0.365128i −0.0139778 + 0.0134679i
\(736\) −6.90600 + 5.01750i −0.254559 + 0.184948i
\(737\) −22.3962 16.2718i −0.824974 0.599378i
\(738\) −17.2697 12.5472i −0.635707 0.461868i
\(739\) −6.93549 + 5.03893i −0.255126 + 0.185360i −0.707996 0.706217i \(-0.750400\pi\)
0.452870 + 0.891577i \(0.350400\pi\)
\(740\) −2.90604 + 0.405094i −0.106828 + 0.0148916i
\(741\) −0.957309 0.695526i −0.0351676 0.0255508i
\(742\) −2.66397 8.19887i −0.0977975 0.300990i
\(743\) 19.8755 0.729162 0.364581 0.931172i \(-0.381212\pi\)
0.364581 + 0.931172i \(0.381212\pi\)
\(744\) −0.283181 0.871542i −0.0103819 0.0319523i
\(745\) 25.9440 + 13.8320i 0.950516 + 0.506767i
\(746\) −8.26351 + 25.4325i −0.302549 + 0.931149i
\(747\) 4.38506 13.4958i 0.160441 0.493787i
\(748\) −1.36750 + 0.993546i −0.0500007 + 0.0363276i
\(749\) 18.4064 0.672555
\(750\) −2.40728 + 1.06210i −0.0879014 + 0.0387823i
\(751\) 20.4537 0.746365 0.373183 0.927758i \(-0.378266\pi\)
0.373183 + 0.927758i \(0.378266\pi\)
\(752\) 9.12876 6.63243i 0.332892 0.241860i
\(753\) −2.14397 + 6.59848i −0.0781308 + 0.240462i
\(754\) 1.42342 4.38084i 0.0518379 0.159541i
\(755\) −27.6238 14.7276i −1.00533 0.535992i
\(756\) 0.432314 + 1.33053i 0.0157231 + 0.0483908i
\(757\) 10.7856 0.392008 0.196004 0.980603i \(-0.437203\pi\)
0.196004 + 0.980603i \(0.437203\pi\)
\(758\) 1.22610 + 3.77354i 0.0445339 + 0.137061i
\(759\) −5.66377 4.11497i −0.205582 0.149364i
\(760\) −14.4359 + 2.01233i −0.523647 + 0.0729949i
\(761\) 30.0238 21.8135i 1.08836 0.790740i 0.109239 0.994016i \(-0.465159\pi\)
0.979122 + 0.203276i \(0.0651587\pi\)
\(762\) −0.606600 0.440720i −0.0219748 0.0159656i
\(763\) −11.0616 8.03675i −0.400458 0.290950i
\(764\) 17.3312 12.5918i 0.627020 0.455556i
\(765\) −2.29986 + 2.21597i −0.0831516 + 0.0801185i
\(766\) −1.79790 1.30625i −0.0649606 0.0471966i
\(767\) 2.50374 + 7.70573i 0.0904049 + 0.278238i
\(768\) −0.235339 −0.00849205
\(769\) 14.3106 + 44.0436i 0.516055 + 1.58825i 0.781354 + 0.624088i \(0.214529\pi\)
−0.265299 + 0.964166i \(0.585471\pi\)
\(770\) −5.61144 + 5.40675i −0.202222 + 0.194846i
\(771\) −1.50769 + 4.64020i −0.0542982 + 0.167113i
\(772\) 6.79724 20.9197i 0.244638 0.752918i
\(773\) −39.5991 + 28.7705i −1.42428 + 1.03480i −0.433236 + 0.901280i \(0.642628\pi\)
−0.991046 + 0.133521i \(0.957372\pi\)
\(774\) −23.1255 −0.831230
\(775\) 12.0211 15.3154i 0.431811 0.550145i
\(776\) 1.10061 0.0395097
\(777\) 0.249831 0.181513i 0.00896265 0.00651175i
\(778\) 0.284313 0.875024i 0.0101931 0.0313711i
\(779\) −14.6023 + 44.9412i −0.523181 + 1.61019i
\(780\) 0.0709356 0.399674i 0.00253990 0.0143106i
\(781\) −0.347426 1.06927i −0.0124319 0.0382614i
\(782\) 4.14050 0.148064
\(783\) −2.58160 7.94534i −0.0922588 0.283943i
\(784\) −0.809017 0.587785i −0.0288935 0.0209923i
\(785\) 6.41853 + 3.42203i 0.229087 + 0.122138i
\(786\) 1.44506 1.04990i 0.0515435 0.0374486i
\(787\) −10.5415 7.65882i −0.375762 0.273007i 0.383834 0.923402i \(-0.374603\pi\)
−0.759596 + 0.650395i \(0.774603\pi\)
\(788\) 1.94035 + 1.40975i 0.0691221 + 0.0502202i
\(789\) −3.18725 + 2.31568i −0.113469 + 0.0824402i
\(790\) 0.418847 2.35992i 0.0149019 0.0839621i
\(791\) 7.29979 + 5.30360i 0.259550 + 0.188574i
\(792\) 3.17100 + 9.75934i 0.112677 + 0.346783i
\(793\) 10.0811 0.357990
\(794\) 8.42926 + 25.9426i 0.299143 + 0.920668i
\(795\) 1.98412 + 4.07965i 0.0703694 + 0.144690i
\(796\) 0.152454 0.469204i 0.00540358 0.0166305i
\(797\) 1.81732 5.59313i 0.0643727 0.198119i −0.913697 0.406396i \(-0.866785\pi\)
0.978070 + 0.208277i \(0.0667855\pi\)
\(798\) 1.24105 0.901678i 0.0439328 0.0319190i
\(799\) −5.47316 −0.193626
\(800\) −2.78666 4.15145i −0.0985232 0.146776i
\(801\) −36.0333 −1.27317
\(802\) −7.38078 + 5.36245i −0.260624 + 0.189355i
\(803\) −8.08714 + 24.8897i −0.285389 + 0.878337i
\(804\) −0.577705 + 1.77799i −0.0203741 + 0.0627050i
\(805\) 18.9049 2.63529i 0.666311 0.0928818i
\(806\) 0.928181 + 2.85665i 0.0326938 + 0.100621i
\(807\) 0.587644 0.0206861
\(808\) −4.05263 12.4727i −0.142571 0.438788i
\(809\) −25.7185 18.6856i −0.904215 0.656951i 0.0353303 0.999376i \(-0.488752\pi\)
−0.939545 + 0.342425i \(0.888752\pi\)
\(810\) 8.31727 + 17.1016i 0.292239 + 0.600889i
\(811\) 26.0990 18.9620i 0.916459 0.665846i −0.0261814 0.999657i \(-0.508335\pi\)
0.942640 + 0.333811i \(0.108335\pi\)
\(812\) 4.83111 + 3.51000i 0.169539 + 0.123177i
\(813\) 2.49428 + 1.81220i 0.0874783 + 0.0635567i
\(814\) 3.69947 2.68782i 0.129666 0.0942081i
\(815\) −8.86857 18.2352i −0.310653 0.638750i
\(816\) 0.0923495 + 0.0670959i 0.00323288 + 0.00234883i
\(817\) 15.8192 + 48.6865i 0.553444 + 1.70333i
\(818\) 34.5433 1.20778
\(819\) −0.701896 2.16021i −0.0245262 0.0754840i
\(820\) −16.0548 + 2.23799i −0.560658 + 0.0781541i
\(821\) 4.18359 12.8758i 0.146008 0.449367i −0.851131 0.524953i \(-0.824083\pi\)
0.997139 + 0.0755861i \(0.0240828\pi\)
\(822\) −0.847949 + 2.60972i −0.0295756 + 0.0910244i
\(823\) −9.78307 + 7.10781i −0.341016 + 0.247763i −0.745091 0.666963i \(-0.767594\pi\)
0.404074 + 0.914726i \(0.367594\pi\)
\(824\) −8.12866 −0.283175
\(825\) 2.53183 3.22565i 0.0881471 0.112303i
\(826\) −10.5038 −0.365473
\(827\) −34.4347 + 25.0183i −1.19741 + 0.869972i −0.994028 0.109127i \(-0.965195\pi\)
−0.203386 + 0.979099i \(0.565195\pi\)
\(828\) 7.76748 23.9058i 0.269938 0.830785i
\(829\) −1.00809 + 3.10257i −0.0350123 + 0.107757i −0.967035 0.254642i \(-0.918042\pi\)
0.932023 + 0.362399i \(0.118042\pi\)
\(830\) −4.71294 9.69053i −0.163588 0.336363i
\(831\) −1.19754 3.68564i −0.0415420 0.127853i
\(832\) 0.771369 0.0267424
\(833\) 0.149888 + 0.461307i 0.00519330 + 0.0159833i
\(834\) −1.47728 1.07331i −0.0511541 0.0371657i
\(835\) 3.99198 22.4921i 0.138148 0.778371i
\(836\) 18.3773 13.3519i 0.635593 0.461785i
\(837\) 4.40721 + 3.20202i 0.152335 + 0.110678i
\(838\) 19.9154 + 14.4694i 0.687967 + 0.499837i
\(839\) −38.7977 + 28.1882i −1.33945 + 0.973165i −0.339982 + 0.940432i \(0.610421\pi\)
−0.999464 + 0.0327330i \(0.989579\pi\)
\(840\) 0.464359 + 0.247573i 0.0160219 + 0.00854207i
\(841\) −5.38783 3.91449i −0.185787 0.134982i
\(842\) −0.558083 1.71760i −0.0192328 0.0591925i
\(843\) −5.34583 −0.184120
\(844\) 1.93047 + 5.94139i 0.0664497 + 0.204511i
\(845\) 4.84736 27.3116i 0.166754 0.939547i
\(846\) −10.2675 + 31.6001i −0.353004 + 1.08644i
\(847\) 0.353594 1.08825i 0.0121496 0.0373927i
\(848\) −6.97437 + 5.06718i −0.239501 + 0.174008i
\(849\) −3.39529 −0.116526
\(850\) −0.0900769 + 2.42356i −0.00308961 + 0.0831275i
\(851\) −11.2012 −0.383973
\(852\) −0.0614251 + 0.0446280i −0.00210439 + 0.00152893i
\(853\) 4.05422 12.4776i 0.138814 0.427225i −0.857350 0.514734i \(-0.827891\pi\)
0.996164 + 0.0875088i \(0.0278906\pi\)
\(854\) −4.03857 + 12.4294i −0.138197 + 0.425327i
\(855\) 30.9070 29.7796i 1.05700 1.01844i
\(856\) −5.68789 17.5055i −0.194408 0.598326i
\(857\) −24.9323 −0.851672 −0.425836 0.904800i \(-0.640020\pi\)
−0.425836 + 0.904800i \(0.640020\pi\)
\(858\) 0.195489 + 0.601654i 0.00667389 + 0.0205401i
\(859\) −41.9386 30.4702i −1.43093 1.03963i −0.989843 0.142162i \(-0.954595\pi\)
−0.441083 0.897466i \(-0.645405\pi\)
\(860\) −12.6460 + 12.1847i −0.431224 + 0.415495i
\(861\) 1.38023 1.00279i 0.0470380 0.0341751i
\(862\) 24.0610 + 17.4814i 0.819522 + 0.595418i
\(863\) 16.6990 + 12.1326i 0.568442 + 0.412997i 0.834539 0.550949i \(-0.185734\pi\)
−0.266097 + 0.963946i \(0.585734\pi\)
\(864\) 1.13181 0.822310i 0.0385051 0.0279756i
\(865\) 31.0470 4.32786i 1.05563 0.147152i
\(866\) 0.261083 + 0.189688i 0.00887198 + 0.00644587i
\(867\) 1.21919 + 3.75229i 0.0414059 + 0.127434i
\(868\) −3.89393 −0.132169
\(869\) 1.15429 + 3.55254i 0.0391566 + 0.120512i
\(870\) −2.77296 1.47840i −0.0940120 0.0501224i
\(871\) 1.89354 5.82772i 0.0641602 0.197465i
\(872\) −4.22517 + 13.0037i −0.143082 + 0.440362i
\(873\) −2.62193 + 1.90494i −0.0887389 + 0.0644726i
\(874\) −55.6427 −1.88214
\(875\) 1.13124 + 11.1230i 0.0382429 + 0.376025i
\(876\) 1.76734 0.0597129
\(877\) −13.3368 + 9.68978i −0.450353 + 0.327200i −0.789735 0.613448i \(-0.789782\pi\)
0.339382 + 0.940649i \(0.389782\pi\)
\(878\) 8.23108 25.3327i 0.277785 0.854936i
\(879\) 2.01548 6.20301i 0.0679805 0.209222i
\(880\) 6.87616 + 3.66602i 0.231795 + 0.123581i
\(881\) 5.63807 + 17.3522i 0.189951 + 0.584610i 0.999998 0.00175471i \(-0.000558542\pi\)
−0.810047 + 0.586365i \(0.800559\pi\)
\(882\) 2.94462 0.0991504
\(883\) 8.56269 + 26.3532i 0.288157 + 0.886857i 0.985434 + 0.170056i \(0.0543947\pi\)
−0.697277 + 0.716802i \(0.745605\pi\)
\(884\) −0.302694 0.219920i −0.0101807 0.00739670i
\(885\) 5.47450 0.763130i 0.184023 0.0256523i
\(886\) −9.73951 + 7.07617i −0.327205 + 0.237729i
\(887\) −4.27713 3.10752i −0.143612 0.104340i 0.513659 0.857994i \(-0.328289\pi\)
−0.657271 + 0.753654i \(0.728289\pi\)
\(888\) −0.249831 0.181513i −0.00838379 0.00609118i
\(889\) −2.57756 + 1.87271i −0.0864486 + 0.0628086i
\(890\) −19.7044 + 18.9857i −0.660494 + 0.636401i
\(891\) −23.9771 17.4204i −0.803264 0.583606i
\(892\) 4.67326 + 14.3828i 0.156472 + 0.481572i
\(893\) 73.5518 2.46132
\(894\) 0.956209 + 2.94291i 0.0319804 + 0.0984255i
\(895\) 10.0714 9.70407i 0.336651 0.324371i
\(896\) −0.309017 + 0.951057i −0.0103235 + 0.0317726i
\(897\) 0.478858 1.47377i 0.0159886 0.0492078i
\(898\) 27.4926 19.9746i 0.917441 0.666560i
\(899\) 23.2529 0.775529
\(900\) 13.8238 + 5.06662i 0.460795 + 0.168887i
\(901\) 4.18149 0.139306
\(902\) 20.4382 14.8492i 0.680517 0.494424i
\(903\) 0.571135 1.75777i 0.0190062 0.0584950i
\(904\) 2.78827 8.58141i 0.0927365 0.285414i
\(905\) −1.16071 + 6.53983i −0.0385834 + 0.217391i
\(906\) −1.01812 3.13345i −0.0338247 0.104102i
\(907\) 47.2539 1.56904 0.784520 0.620103i \(-0.212909\pi\)
0.784520 + 0.620103i \(0.212909\pi\)
\(908\) −2.95729 9.10160i −0.0981411 0.302047i
\(909\) 31.2421 + 22.6987i 1.03624 + 0.752869i
\(910\) −1.52203 0.811468i −0.0504547 0.0268999i
\(911\) 0.867711 0.630429i 0.0287486 0.0208871i −0.573318 0.819333i \(-0.694344\pi\)
0.602067 + 0.798446i \(0.294344\pi\)
\(912\) −1.24105 0.901678i −0.0410954 0.0298575i
\(913\) 13.5865 + 9.87118i 0.449648 + 0.326688i
\(914\) 20.3984 14.8203i 0.674719 0.490212i
\(915\) 1.20184 6.77156i 0.0397317 0.223861i
\(916\) −7.51322 5.45867i −0.248244 0.180360i
\(917\) −2.34540 7.21840i −0.0774519 0.238373i
\(918\) −0.678580 −0.0223965
\(919\) −2.60404 8.01440i −0.0858993 0.264371i 0.898876 0.438203i \(-0.144385\pi\)
−0.984775 + 0.173832i \(0.944385\pi\)
\(920\) −8.34825 17.1653i −0.275234 0.565923i
\(921\) 0.444405 1.36774i 0.0146436 0.0450684i
\(922\) 1.28554 3.95648i 0.0423369 0.130300i
\(923\) 0.201333 0.146277i 0.00662695 0.00481476i
\(924\) −0.820123 −0.0269801
\(925\) 0.243683 6.55641i 0.00801225 0.215574i
\(926\) −10.8531 −0.356655
\(927\) 19.3645 14.0691i 0.636012 0.462090i
\(928\) 1.84532 5.67931i 0.0605756 0.186432i
\(929\) −11.4612 + 35.2740i −0.376031 + 1.15730i 0.566750 + 0.823890i \(0.308200\pi\)
−0.942781 + 0.333413i \(0.891800\pi\)
\(930\) 2.02949 0.282906i 0.0665498 0.00927684i
\(931\) −2.01429 6.19934i −0.0660156 0.203175i
\(932\) −10.8086 −0.354049
\(933\) −1.53964 4.73852i −0.0504055 0.155132i
\(934\) 11.6282 + 8.44840i 0.380487 + 0.276440i
\(935\) −1.65309 3.39900i −0.0540618 0.111159i
\(936\) −1.83759 + 1.33509i −0.0600634 + 0.0436386i
\(937\) 22.4393 + 16.3031i 0.733059 + 0.532599i 0.890530 0.454925i \(-0.150334\pi\)
−0.157470 + 0.987524i \(0.550334\pi\)
\(938\) 6.42670 + 4.66927i 0.209839 + 0.152457i
\(939\) −1.39110 + 1.01069i −0.0453969 + 0.0329828i
\(940\) 11.0352 + 22.6901i 0.359929 + 0.740070i
\(941\) −33.0805 24.0344i −1.07839 0.783498i −0.100990 0.994887i \(-0.532201\pi\)
−0.977402 + 0.211390i \(0.932201\pi\)
\(942\) 0.236565 + 0.728073i 0.00770771 + 0.0237219i
\(943\) −61.8825 −2.01517
\(944\) 3.24585 + 9.98969i 0.105643 + 0.325137i
\(945\) −3.09830 + 0.431894i −0.100788 + 0.0140495i
\(946\) 8.45729 26.0289i 0.274970 0.846271i
\(947\) −11.4471 + 35.2306i −0.371982 + 1.14484i 0.573511 + 0.819198i \(0.305581\pi\)
−0.945493 + 0.325644i \(0.894419\pi\)
\(948\) 0.204079 0.148272i 0.00662817 0.00481565i
\(949\) −5.79281 −0.188042
\(950\) 1.21051 32.5694i 0.0392742 1.05669i
\(951\) 2.53137 0.0820853
\(952\) 0.392411 0.285103i 0.0127181 0.00924026i
\(953\) 13.2075 40.6486i 0.427834 1.31674i −0.472421 0.881373i \(-0.656620\pi\)
0.900255 0.435363i \(-0.143380\pi\)
\(954\) 7.84438 24.1425i 0.253971 0.781643i
\(955\) 20.9506 + 43.0777i 0.677946 + 1.39396i
\(956\) 4.71512 + 14.5116i 0.152498 + 0.469340i
\(957\) 4.89742 0.158311
\(958\) 8.00683 + 24.6425i 0.258689 + 0.796163i
\(959\) 9.43305 + 6.85351i 0.304609 + 0.221311i
\(960\) 0.0919607 0.518136i 0.00296802 0.0167228i
\(961\) 12.8126 9.30892i 0.413310 0.300288i
\(962\) 0.818871 + 0.594945i 0.0264015 + 0.0191818i
\(963\) 43.8485 + 31.8578i 1.41300 + 1.02660i
\(964\) −4.45908 + 3.23971i −0.143617 + 0.104344i
\(965\) 43.4021 + 23.1398i 1.39716 + 0.744896i
\(966\) 1.62525 + 1.18081i 0.0522915 + 0.0379920i
\(967\) 2.09882 + 6.45952i 0.0674937 + 0.207724i 0.979115 0.203307i \(-0.0651689\pi\)
−0.911621 + 0.411031i \(0.865169\pi\)
\(968\) −1.14425 −0.0367777
\(969\) 0.229932 + 0.707657i 0.00738647 + 0.0227332i
\(970\) −0.430075 + 2.42318i −0.0138089 + 0.0778035i
\(971\) −6.55153 + 20.1635i −0.210249 + 0.647079i 0.789208 + 0.614126i \(0.210491\pi\)
−0.999457 + 0.0329533i \(0.989509\pi\)
\(972\) −1.91543 + 5.89508i −0.0614374 + 0.189085i
\(973\) −6.27726 + 4.56070i −0.201240 + 0.146209i
\(974\) 18.4912 0.592495
\(975\) 0.852227 + 0.312352i 0.0272931 + 0.0100033i
\(976\) 13.0691 0.418331
\(977\) 4.64666 3.37599i 0.148660 0.108008i −0.510969 0.859599i \(-0.670713\pi\)
0.659629 + 0.751591i \(0.270713\pi\)
\(978\) 0.659482 2.02968i 0.0210879 0.0649019i
\(979\) 13.1778 40.5571i 0.421164 1.29621i
\(980\) 1.61023 1.55150i 0.0514370 0.0495608i
\(981\) −12.4415 38.2910i −0.397226 1.22254i
\(982\) 7.19251 0.229522
\(983\) −0.465698 1.43327i −0.0148535 0.0457143i 0.943355 0.331785i \(-0.107651\pi\)
−0.958209 + 0.286071i \(0.907651\pi\)
\(984\) −1.38023 1.00279i −0.0440000 0.0319679i
\(985\) −3.86199 + 3.72112i −0.123053 + 0.118565i
\(986\) −2.34331 + 1.70252i −0.0746263 + 0.0542192i
\(987\) −2.14835 1.56087i −0.0683827 0.0496830i
\(988\) 4.06779 + 2.95542i 0.129414 + 0.0940246i
\(989\) −54.2363 + 39.4050i −1.72461 + 1.25300i
\(990\) −22.7258 + 3.16792i −0.722275 + 0.100683i
\(991\) 1.64952 + 1.19844i 0.0523986 + 0.0380698i 0.613676 0.789558i \(-0.289690\pi\)
−0.561278 + 0.827628i \(0.689690\pi\)
\(992\) 1.20329 + 3.70335i 0.0382046 + 0.117582i
\(993\) −5.19293 −0.164793
\(994\) 0.0996959 + 0.306832i 0.00316216 + 0.00973214i
\(995\) 0.973455 + 0.518997i 0.0308606 + 0.0164533i
\(996\) 0.350462 1.07861i 0.0111048 0.0341771i
\(997\) 5.02102 15.4531i 0.159017 0.489405i −0.839528 0.543316i \(-0.817169\pi\)
0.998546 + 0.0539109i \(0.0171687\pi\)
\(998\) 16.3077 11.8482i 0.516210 0.375049i
\(999\) 1.83575 0.0580805
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 350.2.h.d.211.3 yes 20
25.4 even 10 8750.2.a.x.1.6 10
25.16 even 5 inner 350.2.h.d.141.3 20
25.21 even 5 8750.2.a.w.1.5 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
350.2.h.d.141.3 20 25.16 even 5 inner
350.2.h.d.211.3 yes 20 1.1 even 1 trivial
8750.2.a.w.1.5 10 25.21 even 5
8750.2.a.x.1.6 10 25.4 even 10